Ex 12.2, 5 - In a circle of radius 21 cm, an arc subtends 60 - Area of segment of circle and length of arc

  1. Chapter 12 Class 10 Areas related to Circles
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Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find: the length of the arc Length of Arc APB = /360 (2 ) = (60 )/(360 ) 2 22/7 21 = 1/6 2 22/7 21 = 22 cm Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find: (ii) area of the sector formed by the arc Area of sector OAPB = /360 2 = 60/360 22/7 21 21 = 1/6 22/7 21 21 = 1/6 22 3 21 = 231 cm2 Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find: (iii) area of segment formed by the corresponding chord Area of segment APB = Area of sector OAPB Area of OAB From last part, Area of sector OAPB = 231 cm2 Finding area of AOB Area AOB = 1/2 Base Height We draw OM AB OMB = OMA = 90 In OMA & OMB OMA = OMB OA = OB OM = OM OMA OMB AOM = BOM AOM = BOM = 1/2 BOA AOM = BOM = 1/2 60 = 30 Also, since OMB OMA BM = AM BM = AM = 1/2 AB From (1) AM = 1/2AB 2AM = AB AB = 2AM Putting value of AM AB = 2 21/2 AB = 21 Now, Area of AOB = 1/2 Base Height = 1/2 AB OM = 1/2 21 3/2 21 = (441 3)/4 cm2 Area of segment APB = Area of sector OAPB Area of OAB = (231 441/4 3) cm2

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